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arXiv · 2109.04387

Extra-large type Artin groups are hierarchically hyperbolic

Mark Hagen·Alexandre Martin·Alessandro Sisto
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Abstract

We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This implies in particular that these groups have finite asymptotic dimension and uniform exponential growth. We prove these results by using a combinatorial approach to hierarchical hyperbolicity, via the action of these groups on a new complex that is quasi-isometric both to the coned-off Deligne complex introduced by Martin-Przytycki and to a generalisation due to Morris-Wright of the graph of irreducible parabolic subgroups of finite type introduced by Cumplido-Gebhardt-Gonz\'alez-Meneses-Wiest.

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Mark Hagen, Alexandre Martin, Alessandro Sisto. 2021-09-09. Extra-large type Artin groups are hierarchically hyperbolic. https://arxiv.org/abs/2109.04387

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